Linear Programming for the Malmquist Productivity Growth Index

Data Envelopment Analysis

Within couple of days I have been testing DEA modelling (Data Envelopment Analysis) with different R-package. Finally,…. I have found such a comprehensive way to calculate Malmquist indices.

Chart 1

My primary purpose is to show how to use nonparametric methods for measuring efficiency and productivity by using R-programs nonparaeff -package.

At this same time I will show you how to present Malmquist indices within googleVis -world map and finally I will introduse how to make forecast chart for productivity (Chart 1), effectiveness and technical effectiveness indices. In this work I used R-program forecast -library.

First of all I would like to thank Author Dong-hyun Oh for nice work with this nonparaeff-package.

In this working paper I will use example of faremalm2. Like nonpraeff -package documentation we calculate Malmquist productivity growth index of OECD countries
(productivity, technical efficiency and efficiency). As data source we have used Penn World Table (like original sources) with following version:
OECD Timeseries 1980-1990 version pwt5.6
OECD Timeseries 1990-2009 version pwt7.0
In pwt7.0 I cannot find capital stock data, so I downloaded it from here (http://www.ifw-kiel.de/forschung/datenbanken/netcap)

Productivity calculation 1980-1990 As output variables is used Total GDP of a country. This variables is calculated using GDP per capita (rgdpl)
and amount of total population (pop). As input variables is used Total labor force (gdp/rgdpwok) and Total capital stock (kapw * labor)

In second productivity computing calculation 1990-2009 I only use one input and one output variables (labor and gdp). This is because there is no
capital stock data available in pwt7.0 (please correct this If I missed something). I will re-calculate this period asap when I get capital data from all countries.

Note! I encounter problem (NA or other reason) thats why I do this out of box. my.dat is transformed into data.frame and after
that modified with Excel. This is only used in timeseries 1992-2002 productivity calculation.

my.dat$capital <- with(my.dat, kapw * labor) ## Total capital stock MISSING pwt7 note: this is used in pwt5.6
#my.dat$capital <- as.numeric(my.dat$capital)
## Total capital stock ADDED FROM DIFF. SOURCE now used in time
series 1993-2002

my.dat$kapw <- as.numeric(my.dat$kapw) ## Capital stock per labor MISSING pwt7 note: this is used in pwt5.6
#my.dat$kapw <- with(my.dat, my.dat$capital/my.dat$labor) ##
Capital stock per labor now used in time series 1993-2002